%I #14 Jul 02 2018 08:27:04
%S 1,1,1,1,4,5,17,19,64,68,245,251,900,923,3411,3425,12800,12869,48532,
%T 48619,184500,184735,705179,705431,2703168,2704150,10399675,10400530,
%U 40113164,40116599,155113825,155117519,601067520,601080137,2333593349
%N Number of 2n-bead balanced binary necklaces of fundamental period 2n equivalent to reverse.
%H Andrew Howroyd, <a href="/A045680/b045680.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Lu#Lyndon">Index entries for sequences related to Lyndon words</a>
%F Moebius transform of A128014. - _Andrew Howroyd_, Sep 28 2017
%t a[0] = 1;
%t a[n_] := DivisorSum[n, MoebiusMu[n/#] Binomial[# - Mod[#, 2], Quotient[#, 2]]&];
%t Table[a[n], {n, 0, 34}] (* _Jean-François Alcover_, Jul 02 2018, after _Andrew Howroyd_ *)
%o (PARI) a(n) = if(n<1, n>=0, sumdiv(n, d, moebius(n/d) * binomial(d-d%2, d\2))); \\ _Andrew Howroyd_, Sep 28 2017
%Y Cf. A128014.
%K nonn
%O 0,5
%A _David W. Wilson_